## Grain boundaries, their engineering, morphological evolution of crystals, growth of bainite and solid-liquid interfacial energy

### May 7, 2009

[1] On the frequency of occurrence of tilt and twist grain boundaries

A. Morawiec

Homophase grain boundaries are frequently classified into twist, tilt and mixed-type boundaries. With small deviations from pure twist and tilt allowed, there are finite probabilities of occurrence of these particular boundary types in a set of random boundaries. These probabilities are determined for the case of cubic crystal symmetry. If the limit on the deviations is 3°, then 3.9% of random boundaries have near-twist character, and as many as 84.0% of random boundaries are near-tilt boundaries.

[2] A study of low-strain and medium-strain grain boundary engineering

V Randle and M Coleman

Grain boundary engineering (GBE) processing schedules, involving low-strain (5% deformation) iterative treatments, have been carried out on copper. Misorientation and grain boundary plane statistics have been derived, plus tensile and hardness measurements. The Σ3 length fraction and Σ9/Σ3 number ratio decreased during the first two processing iterations, whereas maximum GBE misorientation statistics were achieved after three processing iterations. Analysis of mechanical properties data revealed an accumulation of strain energy throughout the first three processing iterations, sufficient to provide enough driving force for extensive Σ3n interactions. The density of Σ3 boundaries had a larger effect on the rate of hardening than did the density of grain boundaries. This finding indicates the effectiveness of Σ3 interfaces as barriers to plastic flow, which plays an important role in the early stages of GBE processing. Data from samples that had undergone the low-strain iterations were also compared to medium-strain (25% deformation) processing iterations.

[3] Phase-field model study of the crystal morphological evolution of hcp metals

R S Qin and H K D H Bhadeshia

An expression for anisotropic interfacial energy of hexagonal close-packed metals has been formulated which is able to reproduce published data obtained using the modified embedded-atom method, covering the variation in interface energy as a function of orientation for a number of metals. The coefficients associated with the expression can be determined fully by measured or calculated interfacial energies of just three independent crystal planes. Three-dimensional phase-field model simulations using this representation of interfacial energy have been found to yield convincing crystal morphologies. The apparent rate of crystal growth as a function of orientation in the phase-field simulation agrees with predictions made by surface energy theory.

[4] Metallographic evidence of carbon diffusion in the growth of bainite

A Borgenstam, M Hillert and J Agren

There are two paradigms regarding the formation of bainite. One is based on the first stage being rapid, diffusionless growth of acicular ferrite and the subsequent formation of carbide occurring by precipitation from the supersaturated ferrite. An assumption that the first stage occurs as a series of subsequent rapid steps resulting in sub-units plays an important role as an explanation of the not so rapid growth observed macroscopically. The other paradigm is based on the first stage being the formation of acicular ferrite under carbon diffusion and on the subsequent growth of carbide and ferrite side by side. Metallographic observations are presented that support the second paradigm. It is difficult to see how they can be accounted for by the first paradigm, in particular the observation of the shapes of sub-units.

[5] Temperature and structure dependency of solid–liquid interfacial energy

K Mondal et al

A new model has been proposed for the prediction of solid–liquid interfacial energy for pure elements. It is assumed that the interface between crystalline solid embryo and bulk liquid consists of a monolayer of atoms having a similar atomic packing factor as that of the crystalline solids. It has been observed that the solid–liquid interfacial energy is a strong function of temperature and structure of the solid and planar density of the interface. The solid–liquid interfacial energy has a lower value close to melting temperature and it reaches a maximum at some intermediate temperature. This model tries to correlate the classical nucleation phenomena and structure model of interfaces.